a. Is b in {a1, a2, a3}? How many vectors are in {a¡, a2, a3}? b. Is b in W? How many vectors are in W? c. Show that a¡ is in W. [Hint: Row operations are unnec- essary.]

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A: Calculation:Let us assume that

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A: We need to determine type of the set.

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A: For any two nonparallel vectors a and b , it holds that

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A: This is arithmetic progression.

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A: The rank of a matrix is the number of nonzero rows in the reduced matrix.

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Q: Let a, b, and c be n-vectors and let k be a real number.(a) Show that a · b = b · a.(b) Show that (a…

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Q: linear algebra

A: To prove the linear independence of the three given vectors.

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A: Orthogonal vector ( Perpendicular vector): two vectors u and v are orthogonal if u.v=0

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.